cp's OEIS Frontend

A285183 Nearest integer to n*omega(n)/phi(n).

%I A285183 #36 Aug 12 2025 12:44:44
%S A285183 0,2,2,2,1,6,1,2,2,5,1,6,1,5,4,2,1,6,1,5,4,4,1,6,1,4,2,5,1,11,1,2,3,4,
%T A285183 3,6,1,4,3,5,1,11,1,4,4,4,1,6,1,5,3,4,1,6,3,5,3,4,1,11,1,4,4,2,3,10,1,
%U A285183 4,3,9,1,6,1,4,4,4,3,10,1,5,2,4,1,11,3,4,3,4,1,11,3,4,3,4,3,6
%N A285183 Nearest integer to n*omega(n)/phi(n).
%C A285183 n*omega(n)/phi(n) appears in certain bounds of Erdős for the Jacobsthal function g(n) (A048669).
%D A285183 József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter I, p. 34, section I.32.3.
%H A285183 Vincenzo Librandi, <a href="/A285183/b285183.txt">Table of n, a(n) for n = 1..10000</a>
%H A285183 Paul Erdős, <a href="https://doi.org/10.7146/math.scand.a-10523">On the integers relatively prime to n and on a number theoretic function considered by Jacobsthal</a>, Math. Scand., 10, 1962, 163-170.
%p A285183 Digits:=30;
%p A285183 A001221 := proc(n) nops(numtheory[factorset](n)) end proc:
%p A285183 with(numtheory);
%p A285183 f:=n->round(n*A001221(n)/phi(n));
%p A285183 t1:=[seq(f(n),n=1..130)];
%t A285183 Round[Table[(n PrimeNu[n] + 1/2)/EulerPhi[n], {n, 1, 100}]] (* _Vincenzo Librandi_, Apr 21 2017 - confirmed by _Giovanni Resta_ *)
%o A285183 (Magma) [Round(n*#PrimeDivisors(n)/EulerPhi(n)): n in [1..100]]; // _Vincenzo Librandi_, Apr 21 2017
%o A285183 (PARI) a(n) = {my(f = factor(n)); round(n*omega(f)/eulerphi(f));} \\ _Amiram Eldar_, Apr 25 2024
%Y A285183 Cf. A000010 (phi), A001221 (omega), A048669.
%K A285183 nonn
%O A285183 1,2
%A A285183 _N. J. A. Sloane_, Apr 19 2017